The giant graviton expansion in $AdS_5 \times S^5$
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929522567282688 |
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| author | Eleftheriou, Giorgos Murthy, Sameer Rosselló, Martí |
| author_facet | Eleftheriou, Giorgos Murthy, Sameer Rosselló, Martí |
| contents | The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual $AdS_5 \times S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_14921 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The giant graviton expansion in $AdS_5 \times S^5$ Eleftheriou, Giorgos Murthy, Sameer Rosselló, Martí High Energy Physics - Theory The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual $AdS_5 \times S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics. |
| title | The giant graviton expansion in $AdS_5 \times S^5$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.14921 |